To understand the change in the spectrum, let us begin with the easier case in which \(A\)  is a symmetric bounded operator from \(H\)  to \(H\) ; we will denote its norm by \(\Vert A\Vert \) . This is a quite standard situation and is treated for example in [1]} using the resolvent formalism. While not directly relevant for our applications, it will be instructive to discuss this case in detail.
